Michael Francis Atiyah

Sir Michael Francis Atiyah is a British mathematician and one of the most influential mathematicians of the twentieth century.

Michael F. Atiyah was born in London on 22nd April 1929. His father, Edward Atiyah, was Lebanese with an Oxford education. His mother, Jean, came from a Scottish family. Both parents were from middle class professional families, one grandfather being a minister of the church in Yorkshire and the other a doctor in Khartoum. He has two brothers, Patrick and Joe and one sister, Selma.

He went to primary school at the Diocesan school in Khartoum, Sudan (1934−1941) and to secondary school at Victoria College in Cairo and Alexandria (1941−1945); the school was also attended by European nobility displaced by the Second World War and some future leaders of Arab nations. He returned to England and Manchester Grammar School for his HSC studies (1945−1947) and did his national service with the Royal Electrical and Mechanical Engineers (1947−1949). His undergraduate and postgraduate studies took place at Trinity College, Cambridge (1949−1955). He was a doctoral student of William V. D. Hodge and was awarded a doctorate in 1955 for a thesis entitled “Some Applications of Topological Methods in Algebraic Geometry”.

Atiyah married Lily Brown on 30 July 1955, with whom he has three sons.

He spent the academic year 1955−1956 at the Institute for Advanced Study, Princeton, then returned to Cambridge University, where he was a research fellow and assistant lecturer (1957−1958), then a university lecturer and tutorial fellow at Pembroke College (1958−1961).

Atiyah has been active on the international scene, for instance as president of the Pugwash Conferences on Science and World Affairs from 1997 to 2002. He also contributed to the foundation of the Inter Academy Panel on International Issues, the Association of European Academies (ALLEA), the European Mathematical Society (EMS), the Isaac Newton Institute for Mathematical Sciences in Cambridge and was its first director (1990−1996). He was president of the Royal Society (1990−1995), Master of Trinity College, Cambridge (1990−1997), Chancellor of the University of Leicester (1995−2005), and president of the Royal Society of Edinburgh (2005-2008).

Atiyah has collaborated with many mathematicians. His three main collaborations were with Raoul Bott on the Atiyah–Bott fixed-point theorem and many other topics, his best known result is the Atiyah–Singer index theorem, proved with Singer in 1963, a fundamental and widely used result which can be used to count the number of independent solutions of many important differential equations, and with Friedrich Hirzebruch on he founded topological K-theory, a major tool in algebraic topology, that describes the ways in which high dimensional space can be twisted, all of whom he met at the Institute for Advanced Study in Princeton in 1955. More recently he has worked on topics inspired by theoretical physics, such as instantons and monopoles, which are responsible for some subtle corrections in quantum field theory.

His research work went to various branches of mathematics. Atiyah's early papers on algebraic geometry (and some general papers) are reprinted in the first volume of his collected works

In 1966, when he was thirty-seven years old, he was awarded the Fields Medal, for his work in developing K-theory, a generalized Lefschetz fixed-point theorem and the Atiyah-Singer theorem, for which he also won the Abel Prize jointly with Isadore Singer in 2004. Among other prizes he has received are the Royal Medal of the Royal Society in 1968, the De Morgan Medal of the London Mathematical Society in 1980, the Antonio Feltrinelli Prize from the Accademia Nazionale dei Lincei in 1981, the King Faisal International Prize for Science in 1987, the Copley Medal of the Royal Society in 1988, the Benjamin Franklin Medal of the American Philosophical Society in 1993, the Jawaharlal Nehru Birth Centenary Medal of the Indian National Science Academy in 1993, and the President's Medal from the Institute of Physics in 2008.

He is now retired and an honorary professor at the University of Edinburgh.

The 80th birthday on 22nd April, 2009, of Sir Michael Atiyah, was celebrated with the Atiyah80: Geometry and Physics conference organized by ICMS at the Informatics Forum of the University of Edinburgh and the Royal Society of Edinburgh, and a sequence of events Science, Politics and Drama at the Royal Society of Edinburgh and the Royal Lyceum Theatre.

A twisted cubic curve , the subject of Atiyah's first paper

Quotation

“It is hard to communicate understanding because that is something you get by living with a problem for a long time. You study it, perhaps for years; you get out and feel it in your bones. You can’t convey that to anyone else. Having studied the problem for five years you may be able to present it in such a way that it would take someone else less time to get to that point than it took you. But if they haven’t struggled with the problem and seen all the pitfalls, then they haven’t really understood it.” – Michael Atiyah

Sources

MacTutor History of Mathematics archive. St Andrews : University of St Andrews, 1998. [Consult. 25 and 26 March. 2010]. Available in WWW:http://www-groups.dcs.st- and.ac.uk/~history/Biographies/Atiyah.html

Wikipedia . [s.l.] : Wikipedia Foundation, [s.d.], mod. 24 Feb. 2010. [Consult. 24 and 25 March 2010] Available in WWW: http://pt.wikipedia.org/wiki/Michael_Atiyah

Wapedia . [s.l.] :Wapedia, [s.d.]. [Consult. 24 and 25 March 2010]. Available in WWW: http://wapedia.mobi/en/Michael_Atiyah

Available books in the Mathematical Library

SHANAHAN, Patrick D. - The Atiyah-Singer index theorem. - Berlin : Springer, 1978. - IV, 224 p. - (Lecture notes in mathematics ; 638) SP/LNM.638 (UCMA) - 11163

BOOSS-BAVNBEK, Bernhelm, ; BLEECKER, David - Topology and analysis : the Atiyah-Singer index formula and Gauge-theoretic physics. - New York : Springer, 1985. - XVI, 451 p.. - (Universitext)

58G/BOO.Top/ed.ing

YAU, Shing-Tung, ed. lit - The founders of index theory : reminiscences of Atiyah, Bott, Hirzebruch, and Singer / ed. by S. - T. Yau. - Somerville, MA : International Press, 2003. - LIII, 358 p. : fotog. color.

01A70/Fou

PORTUGAL. Laboratório Nacional de Engenharia Civil. Departamento de Barragens de Betão. Núcleo de Modelação Matemática e Física - Teorema do índice de Atiyah-Singer =[Atiyah-Singer index theorem] =[Theoreme de l'index de Atiyah-Singer] / Laboratório Nacional de Engenharia Civil, Departamento de Barragens de Betão, Núcleo de Modelação Matemática e Física. - Lisboa : LNEC, 2008. - ix, 111 p. - (I&D barragens : relatório ; 382/2008-NMMF)

58J/Teo

ATIYAH, Michael Francis - Collected works. - Oxford : Clarendon, 1988. - 5 v

01A75/ATI/V.1 (5 vols.)

ATIYAH, Michael Francis, ; MACDONALD, Ian Grant - Introduction to commutative algebra. - Reading : Addison- Wesley, 1969. - IX, 128 p

13-01/ATI

ATIYAH, Michael Francis, ; MACDONALD, I. G -Introduccion al álgebra commutativa. - Barcelona : Reverté, 1973. - VIII, 146 p.

13-01/ATI/trd.esp

ATIYAH, Michael Francis, ed. lit. ; IAGOLNITZER, Daniel, ed. lit. - Fields medallists' lectures / ed. Michael Atiyah. - Singapore : World Scientific, 1997. - X, 632 p. - (World Scientific series in 20th century mathematics ; 5)

01-06/Fie

ATIYAH, Michael Francis - The geometry and physics of knots. - Cambridge : Cambridge Univ.Press, 1991 reprinted. - X, 78 p.

57M/ATI

SRC/LMS RESEARCH SYMPOSIUM ON REPRESENTATIONS OF LIE GROUPS Oxford 1977 - Representation theory of Lie groups / M. F. Atiyah...[et al.]. - Cambridge : Cambridge University Press, 1979. - V, 341 p. - (London Mathematical Society lecture note series ; 34)

22E/SRC

ATIYAH, Michael Francis - Elliptic operators and compact groups. - Berlin : Springer, 1974. - VI, 93 p. - (Lecture notes in mathematics ; 401)

SP/LNM.401